Name: brook trout growth vs water temperature
Uploaded: 2026-07-24T11:46:38.212Z
Duration: 1 min 26 s
Channel: JoVE

Considere que a temperatura da água afetou a taxa de crescimento da truta-de-riacho. A quantidade de peso que ganhou ao longo de um período fixo em várias temperaturas da água é contabilizada. A resposta da taxa de crescimento às mudanças de temperatura é estimada usando derivadas.No primeiro ponto de dados, a derivada é aproximada usando a inclinação de uma linha secante dianteira traçada entre o primeiro e o segundo pontos.No segundo ponto, a derivada é estimada usando uma diferença central calculando a inclinação da linha secante que conecta os pontos anterior e seguinte, o que fornece uma estimativa mais precisa da derivada.No terceiro ponto, novamente use uma diferença central para calcular a inclinação da linha secante que conecta os pontos antes e depois dela.De forma semelhante, no quarto ponto, a derivada é calculada usando a inclinação da linha secante entre os pontos de dados vizinhos.Finalmente, no último ponto, a derivada é aproximada usando a inclinação da linha secante para trás traçada entre os dois últimos pontos de dados.Essas estimativas derivadas são compiladas em uma tabela. O gráfico correspondente mostra uma queda consistente na taxa de crescimento, mostrando uma correlação negativa entre temperatura e ganho de peso.

taxa de variação: resolução de problemas

Rate of Change: Problem Solving

Crescimento da truta-de-riacho em fun&#xE7;&#xE3;o da temperatura
O crescimento da truta-de-riacho &#xE9; fortemente influenciado pela temperatura da &#xE1;gua. Dados experimentais demonstram como o peso das trutas varia ao longo de um per&#xED;odo de 24 dias em resposta a diferentes temperaturas da &#xE1;gua. Em temperaturas mais baixas, como 15,5 &#xB0;C, as trutas-de-riacho apresentam um ganho de peso significativo. No entanto, &#xE0; medida que a temperatura aumenta, o ganho de peso diminui de forma constante. Na temperatura mais alta registrada, 24,4 &#xB0;C, as trutas apresentam uma perda l&#xED;quida de peso. Esse padr&#xE3;o sugere que a truta-de-riacho prospera em &#xE1;guas mais frias e enfrenta estresse metab&#xF3;lico ou redu&#xE7;&#xE3;o da efici&#xEA;ncia de crescimento em condi&#xE7;&#xF5;es mais quentes.
Estimativa das varia&#xE7;&#xF5;es na taxa de crescimento
Para entender como a taxa de ganho de peso varia com a temperatura, os cientistas estimam a taxa pela qual o peso varia entre valores sucessivos de temperatura. Isso &#xE9; feito comparando a varia&#xE7;&#xE3;o de peso em pequenos intervalos de temperatura. Quando apenas um ponto de temperatura adjacente est&#xE1; dispon&#xED;vel, a estimativa utiliza a varia&#xE7;&#xE3;o entre esses dois pontos. Nos casos em que um ponto de dados experimentais se situa entre outros dois, a m&#xE9;dia das duas taxas de varia&#xE7;&#xE3;o de cada lado fornece uma estimativa melhor. Esses valores permitem compreender a velocidade com que a resposta de crescimento da truta muda com a temperatura.
Interpreta&#xE7;&#xE3;o das tend&#xEA;ncias da taxa de crescimento
As estimativas resultantes mostram que, &#xE0; medida que a temperatura aumenta, a taxa de ganho de peso torna-se mais negativa e decrescente. Isso indica que a truta-de-riacho n&#xE3;o s&#xF3; cresce com menos efici&#xEA;ncia, como tamb&#xE9;m come&#xE7;a a perder peso efetivamente em condi&#xE7;&#xF5;es de temperatura mais elevadas. A taxa de varia&#xE7;&#xE3;o &#xE9; expressa em gramas por grau Celsius, representando quanto o peso das trutas muda para cada aumento de um grau na temperatura. Um gr&#xE1;fico desses valores indica um decl&#xED;nio consistente, confirmando a conclus&#xE3;o de que temperaturas da &#xE1;gua mais elevadas s&#xE3;o cada vez mais desfavor&#xE1;veis ao crescimento da truta-de-riacho.

Taxa de variação: resolução de problemas

Crescimento da truta-de-riacho em fun&#xE7;&#xE3;o da temperatura
O crescimento da truta-de-riacho &#xE9; fortemente influenciado pela temperatura da ...

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Calculus

Cálculo

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Derivatives

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TERMOS-CHAVE E CONCEITOS

brook trout growth vs water temperature

Brook trout growth changes with water temperature. The data show how trout weight shifts over a 24-day period at several temperatures. At cooler water temperatures, such as 15.5 degrees Celsius, the trout gain a lot of weight. As the temperature rises, the amount of weight gained gets smaller.

At the warmest temperature tested, 24.4 degrees Celsius, the trout have a net loss in weight. This pattern suggests that brook trout do better in cooler water. Warmer water may create metabolic stress or reduce growth efficiency.

The rate of change in weight is estimated by comparing nearby temperature values. Rate of change means how much the trout's weight changes for each degree Celsius. When only one nearby point is available, the estimate uses the change between those two points. When a point lies between two others, the two nearby rates are averaged to get a better estimate.

These estimates show that the growth rate becomes more negative as temperature increases. That means the trout grow less efficiently and may begin losing weight in warmer water. A graph of the rates shows a steady decline. The overall trend supports the conclusion that higher water temperatures are less favorable for brook trout growth.

Brook Trout Growth vs Water Temperature

tangent line

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derivatives

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the derivative as a function

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rate of change: problem solving

Brook trout growth changes with water temperature. The data show how trout weight shifts over a 24-day period at several temperatures. At cooler water temperatures, such as 15.5 degrees Celsius, the trout gain a lot of weight. As the temperature rises, the amount of weight gained gets smaller. At the warmest temperature tested, 24.4 degrees Celsius, the trout have a net loss in weight. This pattern suggests that brook trout do better in cooler water. Warmer water may create metabolic stress or...

key terms and concepts

See how brook trout weight changes with water temperature and how rate of change helps show why cooler water supports better growth.

Brook Trout Growth vs Water Temperature | JoVE K12

The JoVE Core Calculus collection provides a comprehensive visual guide to the entire calculus sequence, seamlessly connecting mathematical theory to real-world applications in physics and economics. Through dynamic animated lessons, the course transitions smoothly from foundational single-variable concepts to advanced multivariable topics. Students will explore everything from standard differentiation and integration to spatial vectors, multi-dimensional derivatives, and complex vector fields. By breaking down abstract coordinate systems, infinite series, and spatial motion, this structured approach builds the robust analytical skills and advanced mastery essential for STEM success.

calculus

Brook Trout Growth vs Water Temperature

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